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Example 4: Trigonometric Substitution

07_trigonometric_functions-356.gif.

07_trigonometric_functions-360.gif

 Figure 7.6.5

Put

θ = arcsec (x/a)

(Figure 7.6.5). Then

x = a sec θ, dx = a tan θ sec θ dθ, 07_trigonometric_functions-357.gif = a tan θ.

07_trigonometric_functions-358.gif

 

To keep track of a trigonometric substitution, it is a good idea to actually draw the triangle and label the sides.


Last Update: 2006-11-15